## Tissue Biomechanics Exam (Prof. Thurner) 18.08.2015

nthomas
Beiträge: 4
Registriert: 28.05.2015, 17:44

### Tissue Biomechanics Exam (Prof. Thurner) 18.08.2015

Oral Exam: Duration: ca.45min
Very pleasant talk, at the beginning you can choose if you take the exam in english or german.

Questions:
-) Differences between biological tissues and typical engineering materials (e.g. steel)?
-) Non-linear behaviour in continuum mechanics (types of non-linearities: material, geometrical, boundary)
-) Differences σ-ε between bone and tendons (which amount of elongation is possible until failure occurs?)
-) Lagrange/Euler description -> Green/Almansi strain tensor (explanation, derivation)
-) Hyperelasticity (explanation, strain energy function, stress power)

Hofi
Beiträge: 107
Registriert: 07.11.2010, 11:23

### Tissue Biomechanics- questions and answers-PDF

Thanks for posting your exam questions Thomas!

For all those who still have to do this exam I attached a .pdf-file containing some of the most frequent questions in TBM as found in all forums and FB untill today (including Thomas questions and others). Since I used several books and wrote multiple summaries, the condensed attached .pdf-file might be sometimes overloaded while it lacks proper describtion at other places. Please feel free to correct all errors, change the answers, comment on it and further improve it. Also- if you can remember questions from your exam- please be so kind and post them as well, so that the ones following you can profit from your archivements.

Hofi

ps.: During my examination most of the questions where the same as previously posted. The first half of the exam was about continuum mechanics: why non-linearity (3types of non-lin. in tissue), problem with consti. equations (hierarchy, need RVE), the two descriptions (Lag., Eulerian). How to connect those (def. gradient). What is F? (tensor, contains...) Why do we need strains? What strain measures are there? (GL, Euler, etc.) Whats C? (right CGT). Why symmetric? (because of the $F^TF$ form). Why use squared length? Other strain measures possible? ... Then, after many more questions about Cont. Biomechanics he hooked onto the bone structure in the second half of the exam with questions like: types of bone, hierarchy, where it breaks, osteocyte structure, remodelling, bone cells, length scales, etc....
All the questions are answered ins some way or the other in the attached pdf. For continuum mechanics I can recommend the books by Fung (1965,1993,1994), those by Holzapfel, Humphrey, Lautrup and Epstein, and for bones all books by Cowin as well as Ethiers book from the Introduction to BM lecture.
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reox
Beiträge: 14
Registriert: 30.11.2015, 20:46

### Re: Tissue Biomechanics Exam (Prof. Thurner) 18.08.2015

there is a error in the document regarding 1.5 "strain contains information about both stretch and material rotation": strain measures do not contain the rotational information! Look at the definiton of the r. and l. Cauchy-Green tensor: due to the polar decompostion we get: F=RU=vR, where R is the orthogonal rotation tensor and the defintion of C and b: C=F^TF=U^2, b=FF^T=v^2. Which means there is no rotational part in C and b.
actually the Cauchy Green tensor only contains the quadratic strech, as $\lambda^2 = a_0\cdot C a_o$.
The green-lagrange and almansi strain tensor, depending on C and b, also not contain rotations.